<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We investigate an equivalence relation on permutations based on the pure descent statistic. Generating functions are given for the number of equivalence classes for the set of all permutations, and the sets of permutations avoiding exactly one pattern of length three. As a byproduct, we exhibit a permutation set in one-to-one correspondence with forests of ordered binary trees, which provides a new combinatorial class enumerated by the single-source directed animals on the square lattice. Furthermore, bivariate generating functions for these sets are given according to various statistics.</p></abstract>

We investigate an equivalence relation on permutations based on the pure descent statistic. Generating functions are given for the number of equivalence classes for the set of all permutations, and the sets of permutations avoiding exactly one pattern of length three. As a byproduct, we exhibit a permutation set in one-to-one correspondence with forests of ordered binary trees, which provides a new combinatorial class enumerated by the single-source directed animals on the square lattice. Furthermore, bivariate generating functions for these sets are given according to various statistics.

Forests and pattern-avoiding permutations modulo pure descents

Pure Mathematics and Applications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Forests and pattern-avoiding permutations modulo pure descents"}

We investigate an equivalence relation on permutations based on the pure descent statistic. Generating functions are given for the number of equivalence...

Forests and pattern-avoiding permutations modulo pure descents

Published Online: Aug 06, 2018

Page range: 18 - 31

Received: Jun 16, 2017

DOI: https://doi.org/10.1515/puma-2015-0025

Keywords
permutation, equivalence class, pure descent, pattern, Catalan and Motzkin numbers, forest, directed animal

© 2018 Jean-Luc Baril et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Forests and pattern-avoiding permutations modulo pure descents

Published Online: Aug 06, 2018

Page range: 18 - 31

Received: Jun 16, 2017

DOI: https://doi.org/10.1515/puma-2015-0025

Keywordspermutation, equivalence class, pure descent, pattern, Catalan and Motzkin numbers, forest, directed animal

© 2018 Jean-Luc Baril et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
permutation, equivalence class, pure descent, pattern, Catalan and Motzkin numbers, forest, directed animal